{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T13:00:33Z","timestamp":1782046833690,"version":"3.54.5"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T00:00:00Z","timestamp":1613779200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T00:00:00Z","timestamp":1613779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007751","name":"Akademia G\u00f3rniczo-Hutnicza im. Stanislawa Staszica","doi-asserted-by":"crossref","award":["statutory research grant no. 11.11.230.124"],"award-info":[{"award-number":["statutory research grant no. 11.11.230.124"]}],"id":[{"id":"10.13039\/501100007751","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS\/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.<\/jats:p>","DOI":"10.1007\/s11047-020-09836-w","type":"journal-article","created":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T18:15:24Z","timestamp":1613844924000},"page":"289-315","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Understanding measure-driven algorithms solving irreversibly ill-conditioned problems"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3494-4272","authenticated-orcid":false,"given":"Jakub","family":"Sawicki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcin","family":"\u0141o\u015b","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maciej","family":"Smo\u0142ka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Schaefer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,2,20]]},"reference":[{"key":"9836_CR1","first-page":"330","volume-title":"GECCO 2004, Lecture Notes in Computer Science","author":"W Alden","year":"2004","unstructured":"Alden W, Greg C (2004) Bistability of the needle function in the presence of truncation selection. In: Deb K (ed) GECCO 2004, Lecture Notes in Computer Science, vol 3103. Springer, Berlin, pp 330\u2013342"},{"key":"9836_CR2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.jocs.2016.07.014","volume":"18","author":"J \u00c1lvarez-Aramberri","year":"2017","unstructured":"\u00c1lvarez-Aramberri J, Pardo D (2017) Dimensionally adaptive hp-finite element simulation and inversion of 2d magnetotelluric measurements. J Comput Sci 18:95\u2013105","journal-title":"J Comput Sci"},{"key":"9836_CR3","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1109\/TEVC.2011.2166157","volume":"16","author":"J Arabas","year":"2012","unstructured":"Arabas J (2012) Approximating the genetic diversity of populations in the quasi-equilibrium state. IEEE Trans Evol Comput 16:632\u2013644. https:\/\/doi.org\/10.1109\/TEVC.2011.2166157","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"9836_CR4","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1080\/17415977.2010.531477","volume":"19","author":"B Barabasz","year":"2011","unstructured":"Barabasz B, Mig\u00f3rski S, Schaefer R, Paszy\u0144ski M (2011) Multi-deme, twin adaptive strategy hp-hgs. Inverse Probl Sci Eng 19(1):3\u201316","journal-title":"Inverse Probl Sci Eng"},{"key":"9836_CR5","series-title":"Lecture notes in computer science","first-page":"597","volume-title":"Parallel problem solving from nature\u2014 PPSN XI","author":"N Beume","year":"2010","unstructured":"Beume N, Laumanns M, Rudolph G (2010) Convergence rates of (1+1) evolutionary multiobjective optimization algorithms. In: Schaefer R, Cotta C, Ko\u0142odziej J, Rudolph G (eds) Parallel problem solving from nature\u2014 PPSN XI, vol 6238. Lecture notes in computer science. Springer, Berlin, pp 597\u2013606"},{"issue":"1","key":"9836_CR6","doi-asserted-by":"publisher","first-page":"257","DOI":"10.2478\/bpasts-2013-0025","volume":"61","author":"A Byrski","year":"2013","unstructured":"Byrski A, Schaefer R, Smo\u0142ka M, Cotta C (2013) Asymptotic guarantee of success for multi-agent memetic systems. Bulletin of the polish academy of sciences: technical sciences 61(1):257\u2013278","journal-title":"Bulletin of the polish academy of sciences: technical sciences"},{"issue":"2","key":"9836_CR7","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1090\/qam\/1052135","volume":"48","author":"E Cabib","year":"1990","unstructured":"Cabib E, Davini C, Chong-Quing R (1990) A problem in the optimal design of networks under transverse loading. Quarterly of Appl. Math. 48(2):251\u2013263","journal-title":"Quarterly of Appl. Math."},{"issue":"2","key":"9836_CR8","first-page":"551","volume":"1541","author":"E Cabib","year":"1998","unstructured":"Cabib E, Schaefer R, Telega H (1998) A parallel genetic clustering for inverse problems. Lect Notes Comput Sci 1541(2):551\u2013556","journal-title":"Lect Notes Comput Sci"},{"key":"9836_CR9","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1177\/1475921710381775","volume":"10","author":"JM Caicedo","year":"2011","unstructured":"Caicedo JM, Yun G (2011) A novel evolutionary algorithm for identifying multiple alternative solutions in model updating. Struct Health Monit 10:491\u2013501","journal-title":"Struct Health Monit"},{"key":"9836_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020138","volume-title":"The magnetotelluric method: theory and practice","author":"A Chave","year":"2012","unstructured":"Chave A, Jones A (2012) The magnetotelluric method: theory and practice. Cambridge University Press, Cambridge"},{"key":"9836_CR11","volume-title":"Toward global optimization","year":"1975","unstructured":"Dixon LCW, Szeg\u00f6 GP (eds) (1975) Toward global optimization. North Holland, Amsterdam"},{"issue":"4","key":"9836_CR12","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1029\/91WR02985","volume":"28","author":"Q Duan","year":"1992","unstructured":"Duan Q, Sorooshian S, Gupta V (1992) Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res 28(4):1015\u20131031","journal-title":"Water Resour Res"},{"issue":"1","key":"9836_CR13","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/MIS.2017.5","volume":"32","author":"P Faliszewski","year":"2017","unstructured":"Faliszewski P, Sawicki J, Schaefer R, Smo\u0142ka M (2017) Multiwinner voting in genetic algorithms. IEEE Intell Syst 32(1):40\u201348. https:\/\/doi.org\/10.1109\/MIS.2017.5","journal-title":"IEEE Intell Syst"},{"issue":"2","key":"9836_CR14","doi-asserted-by":"publisher","first-page":"225","DOI":"10.7494\/csci.2016.17.2.225","volume":"17","author":"P Faliszewski","year":"2016","unstructured":"Faliszewski P, Smo\u0142ka M, Schaefer R, Paszy\u0144ski M (2016) On the computational cost and complexity of stochastic inverse solvers. Comput Sci 17(2):225\u2013264. https:\/\/doi.org\/10.7494\/csci.2016.17.2.225","journal-title":"Comput Sci"},{"issue":"1","key":"9836_CR15","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1515\/jag-2019-0025","volume":"14","author":"Q Fan","year":"2020","unstructured":"Fan Q, Meng X, Xu C, Yu J (2020) Solution method for ill-conditioned problems based on a new improved fruit fly optimization algorithm. J Appl Geodesy 14(1):55\u201364. https:\/\/doi.org\/10.1515\/jag-2019-0025","journal-title":"J Appl Geodesy"},{"key":"9836_CR16","series-title":"Lecture notes in computer science","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/978-3-642-15844-5_62","volume-title":"Parallel problem solving from nature\u2014PPSN XI","author":"E Gajda","year":"2010","unstructured":"Gajda E, Schaefer R, Smo\u0142ka M (2010) Evolutionary multiobjective optimization algorithm as a Markov system. In: Schaefer R, Cotta C, Ko\u0142odziej J, Rudolph G (eds) Parallel problem solving from nature\u2014PPSN XI, vol 6238. Lecture notes in computer science. Springer, Berlin, pp 617\u2013626"},{"issue":"3","key":"9836_CR17","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s11047-014-9440-y","volume":"14","author":"E Gajda-Zag\u00f3rska","year":"2014","unstructured":"Gajda-Zag\u00f3rska E, Schaefer R, Smo\u0142ka M, Paszy\u0144ski M, Pardo D (2014) A hybrid method for inversion of 3D DC logging measurements. Nat Comput 14(3):355\u2013374. https:\/\/doi.org\/10.1007\/s11047-014-9440-y","journal-title":"Nat Comput"},{"key":"9836_CR18","first-page":"8789","volume-title":"Advances in neural information processing systems","author":"T Garipov","year":"2018","unstructured":"Garipov T, Izmailov P, Podoprikhin D, Vetrov DP, Wilson AG (2018) Loss surfaces, mode connectivity, and fast ensembling of DNNs. In: Bengio S, Wallach H, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R (eds) Advances in neural information processing systems, vol 31. Curran Associates Inc, Red Hook, pp 8789\u20138798"},{"issue":"1","key":"9836_CR19","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1109\/TSMCB.2011.2160625","volume":"42","author":"S Ghosh","year":"2012","unstructured":"Ghosh S, Das S, Vasilakos AV, Suresh K (2012) On convergence of differential evolution over a class of continuous functions with unique global optimum. IEEE Trans Syst Man Cybern Part B (Cybernetics) 42(1):107\u2013124. https:\/\/doi.org\/10.1109\/TSMCB.2011.2160625","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybernetics)"},{"key":"9836_CR20","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0004-3702(02)00381-8","volume":"145","author":"J He","year":"2003","unstructured":"He J, Yao X (2003) Towards an analytical framework for analysing the computation time of evolutionary algorithms. Artif Intell 145:59\u201397. https:\/\/doi.org\/10.1016\/S0004-3702(02)00381-8","journal-title":"Artif Intell"},{"key":"9836_CR21","unstructured":"Hill G, Wannamaker P, Stodt J, Unsworth M, Maris V, Bedrosian P, Wallin E, Kordy M, Ogawa Y, Kyle P, et\u00a0al. (2017) Imaging the magmatic system of erebus volcano, antarctica using the magnetotelluric method. In: AGU fall meeting abstracts"},{"key":"9836_CR22","volume-title":"Inverse problems for partial differential equations","author":"V Isakov","year":"2006","unstructured":"Isakov V (2006) Inverse problems for partial differential equations. Springer, Berlin"},{"key":"9836_CR23","doi-asserted-by":"publisher","unstructured":"Isshiki M, Sinclair D, Kaneko S (2006) Lens design: global optimization of both performance and tolerance sensitivity. In: International optical design, p. TuA5. Optical Society of America. https:\/\/doi.org\/10.1364\/IODC.2006.TuA5. http:\/\/www.osapublishing.org\/abstract.cfm?URI=IODC-2006-TuA5","DOI":"10.1364\/IODC.2006.TuA5"},{"issue":"1","key":"9836_CR24","first-page":"53","volume":"9","author":"Y Jin","year":"2005","unstructured":"Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):53\u201359","journal-title":"Soft Comput"},{"key":"9836_CR25","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1109\/4235.942533","volume":"5","author":"I Karcz-Dul\u0119ba","year":"2001","unstructured":"Karcz-Dul\u0119ba I (2001) Dynamics of infinite populations evolving in a landscape of uni- and biomodal fitness functions. IEEE Trans Evol Comput 5:398\u2013409. https:\/\/doi.org\/10.1109\/4235.942533","journal-title":"IEEE Trans Evol Comput"},{"key":"9836_CR26","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1109\/TEVC.2005.856070","volume":"10","author":"I Karcz-Dul\u0119ba","year":"2006","unstructured":"Karcz-Dul\u0119ba I (2006) Dynamics of two-element populations in the space of population states. IEEE Trans Evol Comput 10:199\u2013209. https:\/\/doi.org\/10.1109\/TEVC.2005.856070","journal-title":"IEEE Trans Evol Comput"},{"key":"9836_CR27","unstructured":"Kazimierz G (1996) On asymptotic properties of a selection-with-mutation operator. In: Proc. of the 1th Conf. on evolutionary algorithms and global optimization. Warsaw University of Technology Press, pp 50\u201356"},{"issue":"4","key":"9836_CR28","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1785\/BSSA0890040978","volume":"89","author":"K Koper","year":"1999","unstructured":"Koper K, Wysession M, Wiens D (1999) Multimodal function optimization with a niching genetic algorithm: a seismological example. Bull Seismol Soc Am 89(4):978\u2013988","journal-title":"Bull Seismol Soc Am"},{"key":"9836_CR29","doi-asserted-by":"crossref","unstructured":"Lestari W, Widodo A, Warnana D, Syaifuddin F, Utama W, Rochman J (2018) Mapping of kendeng thrust active fault in east java using magnetotelluric method. In: EAGE-HAGI 1st asia pacific meeting on near surface geoscience and engineering","DOI":"10.3997\/2214-4609.201800424"},{"key":"9836_CR30","doi-asserted-by":"publisher","DOI":"10.7494\/csci.2018.19.2.2781","author":"M \u0141o\u015b","year":"2018","unstructured":"\u0141o\u015b M, Smo\u0142ka M, Schaefer R, Sawicki J (2018) Misfit landforms imposed by ill-conditioned inverse parametric problems. Comput Sci. https:\/\/doi.org\/10.7494\/csci.2018.19.2.2781","journal-title":"Comput Sci"},{"key":"9836_CR31","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1177\/1475921710365400","volume":"9","author":"V Meruane","year":"2009","unstructured":"Meruane V, Heylen W (2009) Damage detection with parallel genetic algorithms and operational modes. Struct Health Monit 9:481\u2013496","journal-title":"Struct Health Monit"},{"issue":"14","key":"9836_CR32","doi-asserted-by":"publisher","first-page":"4819","DOI":"10.1007\/s00500-017-2670-z","volume":"22","author":"ED Nino-Ruiz","year":"2018","unstructured":"Nino-Ruiz ED, Ardila C, Capacho R (2018) Local search methods for the solution of implicit inverse problems. Soft Comput 22(14):4819\u20134832","journal-title":"Soft Comput"},{"issue":"1","key":"9836_CR33","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/BF01530781","volume":"5","author":"E Nix","year":"1992","unstructured":"Nix E, Vose D (1992) Modeling genetic algorithms with Markov chains. Annal Math Artif Intell 5(1):79\u201388","journal-title":"Annal Math Artif Intell"},{"key":"9836_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-40065-5","volume-title":"Numerical optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-0-387-40065-5","edition":"2"},{"key":"9836_CR35","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810633","volume-title":"Markov chains","author":"JR Norris","year":"1997","unstructured":"Norris JR (1997) Markov chains. Cambridge University Press, Cambridge"},{"key":"9836_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5362-2","volume-title":"Handbook of global optimization (Nonconvex optimization and its applications)","year":"2002","unstructured":"Pardalos P, Romeijn H (eds) (2002) Handbook of global optimization (Nonconvex optimization and its applications), vol 2. Kluwer, Amsterdam. https:\/\/doi.org\/10.1007\/978-1-4757-5362-2"},{"issue":"5","key":"9836_CR37","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/j.engappai.2006.11.003","volume":"20","author":"M Paruch","year":"2007","unstructured":"Paruch M, Majchrzak E (2007) Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity boundary element method. Eng Appl Artif Intell 20(5):647\u2013655","journal-title":"Eng Appl Artif Intell"},{"key":"9836_CR38","doi-asserted-by":"crossref","unstructured":"Preuss M (2010) Niching the cma-es via nearest-better clustering. In: Proceedings of the 12th annual conference companion on Genetic and evolutionary computation, GECCO\u201910. ACM , pp 1711\u20131718","DOI":"10.1145\/1830761.1830793"},{"key":"9836_CR39","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-07407-8","volume-title":"Multimodal optimization by means of evolutionary algorithms. Natural computing","author":"M Preuss","year":"2015","unstructured":"Preuss M (2015) Multimodal optimization by means of evolutionary algorithms. Natural computing. Springer, Berlin"},{"key":"9836_CR40","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1109\/72.265965","volume":"5","author":"X Qi","year":"1994","unstructured":"Qi X, Palmieri F (1994) Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part I: Basic properties of selection and mutation. IEEE Trans Neural Netw 5:102\u2013119. https:\/\/doi.org\/10.1109\/72.265965","journal-title":"IEEE Trans Neural Netw"},{"key":"9836_CR41","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/72.265966","volume":"5","author":"X Qi","year":"1994","unstructured":"Qi X, Palmieri F (1994) Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part II: Analysis of the diversification role of crossover. IEEE Trans Neural Netw 5:120\u2013129. https:\/\/doi.org\/10.1109\/72.265966","journal-title":"IEEE Trans Neural Netw"},{"key":"9836_CR42","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF02592070","volume":"39","author":"AHG Rinnooy-Kan","year":"1987","unstructured":"Rinnooy-Kan AHG, Timmer GT (1987) Stochastic global optimization methods. part 1: clustering methods. Math Program 39:27\u201356","journal-title":"Math Program"},{"key":"9836_CR43","volume-title":"Handbook of evolutionary computations, chap. B.2.4","author":"G Rudolph","year":"1997","unstructured":"Rudolph G (1997) Local performance measures. In: B\u00e4ck T, Fogel D, Michalewicz Z (eds) Handbook of evolutionary computations, chap. B.2.4. Oxford University Press, Oxford"},{"key":"9836_CR44","volume-title":"Handbook of evolutionary computations, chap. B.2.3","author":"G Rudolph","year":"1997","unstructured":"Rudolph G (1997) Models of stochastic convergence. In: B\u00e4ck T, Fogel D, Michalewicz Z (eds) Handbook of evolutionary computations, chap. B.2.3. Oxford University Press, Oxford"},{"key":"9836_CR45","unstructured":"Rudolph G (2006) Takeover time in parallel populations with migration. In: Proceedings of the second international conference on bioinspired optimization methods and their applications (BIOMA 2006). Josef Stefan Institute, Ljubljana, pp 63\u201372"},{"key":"9836_CR46","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.jocs.2019.04.005","volume":"34","author":"J Sawicki","year":"2019","unstructured":"Sawicki J, \u0141o\u015b M, Smo\u0142ka M, Alvarez-Aramberri J (2019) Using covariance matrix adaptation evolutionary strategy to boost the search accuracy in hierarchic memetic computations. J Comput Sci 34:48\u201354. https:\/\/doi.org\/10.1016\/j.jocs.2019.04.005","journal-title":"J Comput Sci"},{"key":"9836_CR47","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s12293-018-0258-5","volume":"10","author":"J Sawicki","year":"2018","unstructured":"Sawicki J, \u0141o\u015b M, Smo\u0142ka M, Schaefer R, \u00c1lvarez-Aramberri J (2018) Approximating landscape insensitivity regions in solving ill-conditioned inverse problems. Memet Comput 10:279\u2013289. https:\/\/doi.org\/10.1007\/s12293-018-0258-5","journal-title":"Memet Comput"},{"key":"9836_CR48","unstructured":"Sawicki J, Smo\u0142ka M, \u0141o\u015b M, Schaefer R (2019) Approximation of the objective insensitivity regions using hierarchic memetic strategy coupled with covariance matrix adaptation evolutionary strategy. arXiv preprint arXiv:1905.07288"},{"key":"9836_CR49","volume-title":"Foundation of genetic global optimization, with chapter 6 by Telega H. Studies in computational intelligence series","author":"R Schaefer","year":"2007","unstructured":"Schaefer R (2007) Foundation of genetic global optimization, with chapter 6 by Telega H. Studies in computational intelligence series, vol 74. Springer, Berlin"},{"key":"9836_CR50","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/j.engappai.2004.04.014","volume":"17","author":"R Schaefer","year":"2004","unstructured":"Schaefer R, Adamska K, Telega H (2004) Genetic clustering in continuous landscape exploration. Eng Appl Artif Intell (EAAI) 17:407\u2013416","journal-title":"Eng Appl Artif Intell (EAAI)"},{"issue":"12","key":"9836_CR51","doi-asserted-by":"publisher","first-page":"3763","DOI":"10.1016\/j.camwa.2012.02.052","volume":"64","author":"R Schaefer","year":"2012","unstructured":"Schaefer R, Byrski A, Ko\u0142odziej J, Smo\u0142ka M (2012) An agent-based model of hierarchic genetic search. Comput Math Appl (CAMWA) 64(12):3763\u20133776","journal-title":"Comput Math Appl (CAMWA)"},{"issue":"4","key":"9836_CR52","doi-asserted-by":"publisher","first-page":"971","DOI":"10.2478\/v10006-012-0072-z","volume":"22","author":"R Schaefer","year":"2012","unstructured":"Schaefer R, Byrski A, Smo\u0142ka M (2012) Island model as Markov dynamic system. Int J Appl Math Comput Sci 22(4):971\u2013984","journal-title":"Int J Appl Math Comput Sci"},{"key":"9836_CR53","first-page":"383","volume-title":"Foundations of genetic algorithms","author":"R Schaefer","year":"2003","unstructured":"Schaefer R, Ko\u0142odziej J (2003) Genetic search reinforced by the population hierarchy. In: DeJong K, Poli R, Rowe J (eds) Foundations of genetic algorithms, vol 7. Morgan Kaufman, Burlington, pp 383\u2013399"},{"key":"9836_CR54","doi-asserted-by":"publisher","first-page":"171","DOI":"10.4064\/sm-2-1-171-180","volume":"2","author":"J Schauder","year":"1930","unstructured":"Schauder J (1930) Der Fixpunktsatz in Funktionalr\u00e4umen. Studia Mathematica 2:171\u2013180","journal-title":"Studia Mathematica"},{"key":"9836_CR55","volume-title":"Memetic strategies and autonomous systems for solving inverse problems, Dissertations and Monographs","author":"M Smo\u0142ka","year":"2015","unstructured":"Smo\u0142ka M (2015) Memetic strategies and autonomous systems for solving inverse problems, Dissertations and Monographs, vol 311. AGH University of Science and Technology Press, Krak\u00f3w"},{"key":"9836_CR56","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1016\/j.asoc.2015.06.055","volume":"36","author":"M Smo\u0142ka","year":"2015","unstructured":"Smo\u0142ka M, Gajda-Zag\u00f3rska E, Schaefer R, Paszy\u0144ski M, Pardo D (2015) A hybrid method for inversion of 3D AC logging measurements. Appl Soft Comput 36:422\u2013456","journal-title":"Appl Soft Comput"},{"issue":"3","key":"9836_CR57","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1515\/amcs-2015-0036","volume":"25","author":"M Smo\u0142ka","year":"2015","unstructured":"Smo\u0142ka M, Schaefer R, Paszy\u0144ski M, Pardo D, \u00c1lvarez-Aramberri J (2015) An agent-oriented hierarchic strategy for solving inverse problems. Int J Appl Math Comput Sci 25(3):483\u2013498. https:\/\/doi.org\/10.1515\/amcs-2015-0036","journal-title":"Int J Appl Math Comput Sci"},{"key":"9836_CR58","series-title":"Lecture notes in computer science","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/978-3-642-15844-5_13","volume-title":"Parallel problem solving from nature \u2013 PPSN XI","author":"D Sudholt","year":"2010","unstructured":"Sudholt D (2010) General lower bounds for the running time of evolutionary algorithms. In: Schaefer R, Cotta C, Ko\u0142odziej J, Rudolph G (eds) Parallel problem solving from nature \u2013 PPSN XI, vol 6238. Lecture notes in computer science. Springer, Berlin, pp 124\u2013133"},{"key":"9836_CR59","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717921","volume-title":"Inverse problem theory and methods for model parameter estimation","author":"A Tarantola","year":"2005","unstructured":"Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, Philadelphia"},{"key":"9836_CR60","unstructured":"Telega H (1999) Parallel algorithms for solving selected inverse problems. Ph.D. thesis, AGH University of Science and Technology, Krak\u00f3w, Poland"},{"key":"9836_CR61","unstructured":"Ursem RK (1999) Multinational evolutionary algorithms. In: Proceedings of the 1999 congress on evolutionary computation CEC\u201999, vol 3. IEEE"},{"key":"9836_CR62","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/6229.001.0001","volume-title":"The simple genetic algorithm: foundations and theory","author":"MD Vose","year":"1999","unstructured":"Vose MD (1999) The simple genetic algorithm: foundations and theory, vol 12. MIT Press, Cambridge"},{"issue":"1","key":"9836_CR63","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1190\/1.1440255","volume":"37","author":"K Vozoff","year":"1972","unstructured":"Vozoff K (1972) The magnetotelluric method in the exploration of sedimentary basins. Geophysics 37(1):98\u2013141","journal-title":"Geophysics"},{"key":"9836_CR64","first-page":"31","volume":"4","author":"A Wolny","year":"2011","unstructured":"Wolny A, Schaefer R (2011) Improving population-based algorithms with fitness deterioration. J Telecommun Inf Technol 4:31\u201344","journal-title":"J Telecommun Inf Technol"},{"key":"9836_CR65","volume-title":"Nonlinear functional analysis and its application. II\/A: linear monotone operators","author":"E Zeidler","year":"2000","unstructured":"Zeidler E (2000) Nonlinear functional analysis and its application. II\/A: linear monotone operators. Springer, Berlin"},{"issue":"1","key":"9836_CR66","doi-asserted-by":"publisher","first-page":"F77","DOI":"10.1190\/1.3526299","volume":"76","author":"M Zhdanov","year":"2011","unstructured":"Zhdanov M, Wan L, Gribenko A, \u010cuma M, Key K, Constable S (2011) Large-scale 3d inversion of marine magnetotelluric data: case study from the Gemini prospect, Gulf of Mexico. Geophysics 76(1):F77\u2013F87","journal-title":"Geophysics"}],"container-title":["Natural Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-020-09836-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11047-020-09836-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-020-09836-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,18]],"date-time":"2022-12-18T09:41:24Z","timestamp":1671356484000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11047-020-09836-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,20]]},"references-count":66,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["9836"],"URL":"https:\/\/doi.org\/10.1007\/s11047-020-09836-w","relation":{},"ISSN":["1567-7818","1572-9796"],"issn-type":[{"value":"1567-7818","type":"print"},{"value":"1572-9796","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,20]]},"assertion":[{"value":"15 December 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}